How to use absolute value in Loopcut and edge slide?
When you press Ctrl + R you actually perform two actions: Loop Cut + Edge Slide.
The easiest way to slide edges a certain distance from a vertex is to slide to a vertex first, then slide the desired distance.

Ctrl + R + LMB to select the ring to cut
1 (or -1) to place the loop at the very last vertex of the edge you are cutting
Ctrl + E + Edge Slide + relative distance

NOTE
In this way you can set zero at a vertex instead at the center.
It helps to calculate the absolute distance (as Carlo suggests), but actually doesn't allow to set edge slide by unit.
You don't need to calculate the value manually: use Python expressions instead, simply typing = followed by the operation
Check Edge Info: Length in Property Panel (N)

Even off
If you're sliding proportionally (Even off), you have to choose the edge wich the absolute slide amount refers to.
In this example, I want the edge to slide 0.5 units along the shortest edge.

Now the tricky part: type this simple operation (thanks @Carlo):
= absolute_distance / edge_lenght

in my case:
= 0.5 / 1.13

Even on
From Blender Manual

Even E
Forces the edge loop to match the shape of the adjacent edge loop. You can flip to the opposite vertex using F. Use Alt-Wheel to change the control edge.
Flip F
When Even mode is active, this flips between the two adjacent edge loops the active edge loop will match

In this case, the operation is a bit longer, because zero is at the median point of the edge :
  = absolute_distance / edge_lenght - edge_lenght / 2

in my case:
= 0.5 / 1.13 - 1.13 / 2

note:
You'll notice a rounding error (the value is not exactly 0.5), because some approximation